{"id":"https://openalex.org/W2037568445","doi":"https://doi.org/10.1137/070711499","title":"Inpainting by Flexible Haar-Wavelet Shrinkage","display_name":"Inpainting by Flexible Haar-Wavelet Shrinkage","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2037568445","doi":"https://doi.org/10.1137/070711499","mag":"2037568445"},"language":"en","primary_location":{"id":"doi:10.1137/070711499","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070711499","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Imaging Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004126693","display_name":"Raymond H. Chan","orcid":"https://orcid.org/0000-0003-0910-4685"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"R. H. Chan","raw_affiliation_strings":["rchan@math.cuhk.edu.hk#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"rchan@math.cuhk.edu.hk#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068036295","display_name":"Simon Setzer","orcid":null},"institutions":[{"id":"https://openalex.org/I177802217","display_name":"University of Mannheim","ror":"https://ror.org/031bsb921","country_code":"DE","type":"education","lineage":["https://openalex.org/I177802217"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"S. Setzer","raw_affiliation_strings":["ssetzer@kiwi.math.uni-mannheim.de and steidl@math.uni-mannheim.de#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ssetzer@kiwi.math.uni-mannheim.de and steidl@math.uni-mannheim.de#TAB#","institution_ids":["https://openalex.org/I177802217"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008755474","display_name":"Gabriele Steidl","orcid":"https://orcid.org/0000-0003-4638-9245"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"G. Steidl","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.1018,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.94109644,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"1","issue":"3","first_page":"273","last_page":"293"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/inpainting","display_name":"Inpainting","score":0.9686306715011597},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.7340372800827026},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.7235515713691711},{"id":"https://openalex.org/keywords/shrinkage","display_name":"Shrinkage","score":0.661398708820343},{"id":"https://openalex.org/keywords/haar","display_name":"Haar","score":0.5894879102706909},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5401185750961304},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.532842218875885},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5105165243148804},{"id":"https://openalex.org/keywords/haar-wavelet","display_name":"Haar wavelet","score":0.5093404054641724},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.431735098361969},{"id":"https://openalex.org/keywords/pixel","display_name":"Pixel","score":0.41624945402145386},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.4157816469669342},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4013431668281555},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3877306282520294},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.34832122921943665},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.3320273756980896},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32976746559143066},{"id":"https://openalex.org/keywords/discrete-wavelet-transform","display_name":"Discrete wavelet transform","score":0.21549579501152039},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12867650389671326}],"concepts":[{"id":"https://openalex.org/C11727466","wikidata":"https://www.wikidata.org/wiki/Q1628157","display_name":"Inpainting","level":3,"score":0.9686306715011597},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.7340372800827026},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.7235515713691711},{"id":"https://openalex.org/C180145272","wikidata":"https://www.wikidata.org/wiki/Q7504144","display_name":"Shrinkage","level":2,"score":0.661398708820343},{"id":"https://openalex.org/C187029792","wikidata":"https://www.wikidata.org/wiki/Q2179112","display_name":"Haar","level":3,"score":0.5894879102706909},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5401185750961304},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.532842218875885},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5105165243148804},{"id":"https://openalex.org/C2780423554","wikidata":"https://www.wikidata.org/wiki/Q766198","display_name":"Haar wavelet","level":5,"score":0.5093404054641724},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.431735098361969},{"id":"https://openalex.org/C160633673","wikidata":"https://www.wikidata.org/wiki/Q355198","display_name":"Pixel","level":2,"score":0.41624945402145386},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.4157816469669342},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4013431668281555},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3877306282520294},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.34832122921943665},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.3320273756980896},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32976746559143066},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.21549579501152039},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12867650389671326},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/070711499","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070711499","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Imaging Sciences","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.150.3948","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.150.3948","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.cuhk.edu.hk/~rchan/paper/steidl.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.684.7124","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.684.7124","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mia.uni-saarland.de/setzer/publications/haar_inpaint_aniso.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W572198187","https://openalex.org/W1480546554","https://openalex.org/W1523201499","https://openalex.org/W1549732571","https://openalex.org/W1970986119","https://openalex.org/W1998576973","https://openalex.org/W1999788007","https://openalex.org/W1999905919","https://openalex.org/W2006262045","https://openalex.org/W2016885551","https://openalex.org/W2019569173","https://openalex.org/W2042261731","https://openalex.org/W2067736594","https://openalex.org/W2069435104","https://openalex.org/W2081160575","https://openalex.org/W2084115655","https://openalex.org/W2088950251","https://openalex.org/W2093212899","https://openalex.org/W2101376980","https://openalex.org/W2103559027","https://openalex.org/W2115706991","https://openalex.org/W2154746110","https://openalex.org/W2295936755","https://openalex.org/W2623831436","https://openalex.org/W2792017591","https://openalex.org/W4250507917","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2766849256","https://openalex.org/W4361795924","https://openalex.org/W984746159","https://openalex.org/W1523827626","https://openalex.org/W1999916501","https://openalex.org/W4232769230","https://openalex.org/W2005569824","https://openalex.org/W111100742","https://openalex.org/W4239324723","https://openalex.org/W2043338154"],"abstract_inverted_index":{"We":[0,22],"present":[1],"novel":[2],"wavelet-based":[3],"inpainting":[4],"algorithms.":[5,55],"Applying":[6],"ideas":[7],"from":[8],"anisotropic":[9],"regularization":[10],"and":[11,36],"diffusion,":[12],"our":[13,24,54],"models":[14],"can":[15],"better":[16],"handle":[17],"degraded":[18],"pixels":[19],"at":[20],"edges.":[21],"interpret":[23],"algorithms":[25],"within":[26],"the":[27,39,50],"framework":[28],"of":[29,53],"forward-backward":[30],"splitting":[31],"methods":[32],"in":[33],"convex":[34],"analysis":[35],"prove":[37],"that":[38],"conditions":[40],"for":[41],"ensuring":[42],"their":[43],"convergence":[44],"are":[45],"fulfilled.":[46],"Numerical":[47],"examples":[48],"illustrate":[49],"good":[51],"performance":[52]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
